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March 2012 Stochastic maximal Lp-regularity
Jan van Neerven, Mark Veraar, Lutz Weis
Ann. Probab. 40(2): 788-812 (March 2012). DOI: 10.1214/10-AOP626


In this article we prove a maximal Lp-regularity result for stochastic convolutions, which extends Krylov’s basic mixed Lp(Lq)-inequality for the Laplace operator on ℝd to large classes of elliptic operators, both on ℝd and on bounded domains in ℝd with various boundary conditions. Our method of proof is based on McIntosh’s H-functional calculus, R-boundedness techniques and sharp Lp(Lq)-square function estimates for stochastic integrals in Lq-spaces. Under an additional invertibility assumption on A, a maximal space–time Lp-regularity result is obtained as well.


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Jan van Neerven. Mark Veraar. Lutz Weis. "Stochastic maximal Lp-regularity." Ann. Probab. 40 (2) 788 - 812, March 2012.


Published: March 2012
First available in Project Euclid: 26 March 2012

zbMATH: 1249.60147
MathSciNet: MR2952092
Digital Object Identifier: 10.1214/10-AOP626

Primary: 60H15
Secondary: 35B65 , 35R60 , 42B25 , 42B37 , 47A60 , 47D06

Keywords: H∞-calculus , R-boundedness , square function , stochastic convolutions , Stochastic maximal Lp-regularity , Stochastic partial differential equations

Rights: Copyright © 2012 Institute of Mathematical Statistics


Vol.40 • No. 2 • March 2012
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